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Symmetric graphs and the classification of the finite simple groups

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Groups — Korea 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1098))

Abstract

Some applications of the finite simple group classification to the study of symmetric graphs are discussed.

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References

  1. M. Aschbacher and L.L. Scott, "Maximal subgroups of finite groups", J. Algebra, to appear.

    Google Scholar 

  2. N.L. Biggs and D.H. Smith, "On trivalent graphs", Bull. London Math. Soc. 3 (1971), pp. 155–158, MR44:3902.

    Article  MathSciNet  MATH  Google Scholar 

  3. J.M.J. Buczak, "Finite group theory", D.Phil. Thesis, Oxford University (1980).

    Google Scholar 

  4. P.J. Cameron, "Permutation groups with multiply transitive suborbits", Proc. London Math. Soc. (3) 25 (1972), pp. 427–440, MR47:5082.

    Article  MathSciNet  MATH  Google Scholar 

  5. P.J. Cameron, "Suborbits in transitive permutation groups", Combinatorics (eds. M. Hall, Jr and J.H. van Lint, Math. Centre Tracts 57, Math. Centrum, Amsterdam, 1973), pp. 98–129, MR51:5718.

    Google Scholar 

  6. P.J. Cameron, "6-Transitive graphs", J. Combinatorial Theory (B) 28 (1980), pp. 168–179, MR81g:05076.

    Article  MATH  Google Scholar 

  7. P.J. Cameron, "Finite permutation groups and finite simple groups", Bull. London Math. Soc. 13 (1981), pp. 1–22, MR80m:20008.

    Article  MathSciNet  MATH  Google Scholar 

  8. P.J. Cameron, "Finite simple groups and finite geometries", Proceedings of Pullman Conference on Finite Geometry (1981), to appear.

    Google Scholar 

  9. P.J. Cameron and C.E. Praeger, "Graphs and permutation groups with projective subconstituents", J. London Math. Soc. (2) 25 (1982), pp. 62–74.

    Article  MathSciNet  MATH  Google Scholar 

  10. P.J. Cameron and C.E. Praeger, "On 2-arc transitive graphs of girth 4", J. Combinatorial Theory (B) 35 (1983), pp. 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  11. P.J. Cameron, C.E. Praeger, J. Saxl, and G.M. Seitz, "On the Sims conjecture and distance transitive graphs", Bull. London Math. Soc. 15 (1983), pp. 499–506.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Gardiner, "Arc transitivity in graphs", Quart. J. Math. Oxford (2) 24 (1973), pp. 399–407, MR48:1973.

    Article  MathSciNet  MATH  Google Scholar 

  13. A. Gardiner, "Symmetry conditions in graphs", Surveys in Combinatorics (ed. B. Bollabas, London Math. Soc. Lecture Notes in Math. 38, Cambridge University Press, Cambridge, 1979), pp. 22–43, MR81e:05081.

    Chapter  Google Scholar 

  14. D.G. Higman, "Intersection matrices for finite permutation groups", J. Algebra 6 (1967), pp. 22–42, MR35:244.

    Article  MathSciNet  MATH  Google Scholar 

  15. L.G. Kovács, "Maximal subgroups in composite finite groups", (unpublished).

    Google Scholar 

  16. C.E. Praeger, "Primitive permutation groups and a characterization of the odd graphs", J. Combinatorial Theory (B) 31 (1981), pp. 117–142, MR83c:20003.

    Article  MathSciNet  MATH  Google Scholar 

  17. C.E. Praeger, "When are symmetric graphs characterised by their local properties?", Combinatorial Mathematics IX (eds. E.J. Billington, S. Oates-Williams, and A.P. Street, Lecture Notes in Math. 952, Springer, Berlin-Heidelberg-New York, 1982), pp. 123–141.

    Chapter  Google Scholar 

  18. C.E. Praeger, "Finite simple groups and finite primitive permutation groups", Bull. Austral. Math. Soc. 28 (1983), pp. 355–366.

    Article  MathSciNet  MATH  Google Scholar 

  19. D.H. Smith, "Distance-transitive graphs of valency four", J. London Math. Soc. (2) 8 (1974), pp. 377–384, MR52:2026.

    Article  MathSciNet  MATH  Google Scholar 

  20. J.G. Thompson, "Bounds for the order of maximal subgroups", J. Algebra 14 (1970), pp. 135–138, MR40:5720.

    Article  MathSciNet  MATH  Google Scholar 

  21. W.T. Tutte, "A family of cubical graphs", Proc. Camb. Phil. Soc. 43 (1947), pp. 459–474, MR9,p7.

    Article  MathSciNet  MATH  Google Scholar 

  22. W.T. Tutte, "On the symmetry of cubic graphs", Canad. J. Math. 11 (1959), pp. 621–624, MR22:679.

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Weiss, "s-transitive graphs", Algebraic Methods in Graph Theory (Colloquia Math. Soc. Janos Bolyai 25, North-Holland, Amsterdam, 1981), pp. 827–847, MR83b:05071.

    Google Scholar 

  24. H. Wielandt, Finite Permutation Groups (Academic Press, New York-London, 1964), MR32:1252.

    MATH  Google Scholar 

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Ann Chi Kim Bernhard H. Neumann

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© 1984 Springer-Verlag

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Praeger, C.E. (1984). Symmetric graphs and the classification of the finite simple groups. In: Kim, A.C., Neumann, B.H. (eds) Groups — Korea 1983. Lecture Notes in Mathematics, vol 1098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099667

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  • DOI: https://doi.org/10.1007/BFb0099667

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13890-7

  • Online ISBN: 978-3-540-39102-9

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